In this section, we introduce an iterative
algorithm that simulates single-site dynamics.
The algorithm falls into the general framework of belief propagation (BP):
each site maintains an internal state, which is updated iteratively according to the current internal states of adjacent sites until a fixpoint is reached.
The classic sum-product BP algorithms were known for calculating marginal probabilities [1]}, [2]}.
Here we give a BP style algorithm for simulating the chain itself.
